Volume 18, Issue 4
Convergence Analysis of Yee-FDTD Schemes for 3D Maxwell's Equations in Linear Dispersive Media

​Puttha Sakkaplangkul & Vrushali A. Bokil

Int. J. Numer. Anal. Mod., 18 (2021), pp. 524-568.

Published online: 2021-05

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  • Abstract

In this paper, we develop and analyze finite difference methods for the 3D Maxwell's equations in the time domain in three different types of linear dispersive media described as Debye, Lorentz and cold plasma. These methods are constructed by extending the Yee-Finite Difference Time Domain (FDTD) method to linear dispersive materials. We analyze the stability criterion for the FDTD schemes by using the energy method. Based on energy identities for the continuous models, we derive discrete energy estimates for the FDTD schemes for the three dispersive models. We also prove the convergence of the FDTD schemes with perfect electric conducting boundary conditions, which describes the second order accuracy of the methods in both time and space. The discrete divergence-free conditions of the FDTD schemes are studied. Lastly, numerical examples are given to demonstrate and confirm our results.

  • Keywords

Maxwell's equations, Debye, Lorentz, cold plasma dispersive media, Yee scheme, FDTD method, energy decay, convergence analysis.

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COPYRIGHT: © Global Science Press

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@Article{IJNAM-18-524, author = {Sakkaplangkul , ​Puttha and Bokil , Vrushali A.}, title = {Convergence Analysis of Yee-FDTD Schemes for 3D Maxwell's Equations in Linear Dispersive Media}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2021}, volume = {18}, number = {4}, pages = {524--568}, abstract = {

In this paper, we develop and analyze finite difference methods for the 3D Maxwell's equations in the time domain in three different types of linear dispersive media described as Debye, Lorentz and cold plasma. These methods are constructed by extending the Yee-Finite Difference Time Domain (FDTD) method to linear dispersive materials. We analyze the stability criterion for the FDTD schemes by using the energy method. Based on energy identities for the continuous models, we derive discrete energy estimates for the FDTD schemes for the three dispersive models. We also prove the convergence of the FDTD schemes with perfect electric conducting boundary conditions, which describes the second order accuracy of the methods in both time and space. The discrete divergence-free conditions of the FDTD schemes are studied. Lastly, numerical examples are given to demonstrate and confirm our results.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/19113.html} }
TY - JOUR T1 - Convergence Analysis of Yee-FDTD Schemes for 3D Maxwell's Equations in Linear Dispersive Media AU - Sakkaplangkul , ​Puttha AU - Bokil , Vrushali A. JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 524 EP - 568 PY - 2021 DA - 2021/05 SN - 18 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/19113.html KW - Maxwell's equations, Debye, Lorentz, cold plasma dispersive media, Yee scheme, FDTD method, energy decay, convergence analysis. AB -

In this paper, we develop and analyze finite difference methods for the 3D Maxwell's equations in the time domain in three different types of linear dispersive media described as Debye, Lorentz and cold plasma. These methods are constructed by extending the Yee-Finite Difference Time Domain (FDTD) method to linear dispersive materials. We analyze the stability criterion for the FDTD schemes by using the energy method. Based on energy identities for the continuous models, we derive discrete energy estimates for the FDTD schemes for the three dispersive models. We also prove the convergence of the FDTD schemes with perfect electric conducting boundary conditions, which describes the second order accuracy of the methods in both time and space. The discrete divergence-free conditions of the FDTD schemes are studied. Lastly, numerical examples are given to demonstrate and confirm our results.

​Puttha Sakkaplangkul & Vrushali A.Bokil. (2021). Convergence Analysis of Yee-FDTD Schemes for 3D Maxwell's Equations in Linear Dispersive Media. International Journal of Numerical Analysis and Modeling. 18 (4). 524-568. doi:
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